I'm not a medic, just a lowly EMT-B ("basic") so take what I say with some salt.

EMT-P is indeed paramedic. I believe (though I'm not 100% sure) that some states may allow you to challenge the EMT-P exam with your RN credential. Might be worth looking into. Otherwise, I'm sure there would be a lot of duplication in the coursework (A&P, pharma, etc.).

I don't think you'd have to actually "work" to keep the medic cert, but you would have to take refresher courses every few years. Also, medics do a variety of skills that get rusty if they don't use them, such as starting lines, intubation, etc. You may do all that in your nursing job, so it might not be an issue, but it's something to think about.

You should know that working on a air ambulance is a very dangerous occupation. Not trying to talk you out of it, but go in with your eyes open!